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Minimal energy for geometrically nonlinear elastic inclusions in two dimensions

We are concerned with a variant of the isoperimetric problem, which in our setting arises in a geometrically nonlinear two-well problem in elasticity. More precisely, we investigate the optimal scaling of the energy of an elastic inclusion of a fixed volume for which the energy is determined by a su...

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Hauptverfasser: Akramov, Ibrokhimbek (VerfasserIn) , Knüpfer, Hans (VerfasserIn) , Kružík, Martin (VerfasserIn) , Rüland, Angkana (VerfasserIn)
Dokumenttyp: Article (Journal)
Sprache:Englisch
Veröffentlicht: 2024
In: Proceedings. Section A, Mathematics
Year: 2024, Jahrgang: 154, Heft: 3, Pages: 769-792
ISSN:1473-7124
DOI:10.1017/prm.2023.36
Online-Zugang:Verlag, kostenfrei, Volltext: https://doi.org/10.1017/prm.2023.36
Verlag, kostenfrei, Volltext: https://www.cambridge.org/core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics/article/minimal-energy-for-geometrically-nonlinear-elastic-inclusions-in-two-dimensions/8E4138F662DB9421EEF5E96FB8A95D34
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Verfasserangaben:Ibrokhimbek Akramov, Hans Knüpfer, Martin Kružík, Angkana Rüland
Beschreibung
Zusammenfassung:We are concerned with a variant of the isoperimetric problem, which in our setting arises in a geometrically nonlinear two-well problem in elasticity. More precisely, we investigate the optimal scaling of the energy of an elastic inclusion of a fixed volume for which the energy is determined by a surface and an (anisotropic) elastic contribution. Following ideas from Conti and Schweizer (Commun. Pure Appl. Math. 59 (2006), 830-868) and Knüpfer and Kohn (Proc. R. Soc. London Ser. A Math. Phys. Eng. Sci. 467 (2011), 695-717), we derive the lower scaling bound by invoking a two-well rigidity argument and a covering result. The upper bound follows from a well-known construction for a lens-shaped elastic inclusion.
Beschreibung:Online publiziert von Cambridge University Press: 12 Mai 2023
Gesehen am 09.12.2024
Beschreibung:Online Resource
ISSN:1473-7124
DOI:10.1017/prm.2023.36

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